Finite Group Databasebeta

← C29×#8426 #20303326

Subgroups — C29×#8426 #20303326

Order 7424.

836 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3508C211yesmaximal, characteristic
2C29×#1982C211yesmaximal, characteristic, complemented
3C29×#1806C211yesmaximal, characteristic, complemented
4C29×#1550C211yesmaximal, characteristic, complemented
5C29×#1545C211yesmaximal, characteristic, complemented
6C29×#1503C211yesmaximal, characteristic, complemented
7C29×#1477C211yesmaximal, characteristic, complemented
8C29×#559—21no—
9C29×#559C412yescomplemented
10C29×#550—21no—
11C29×#550C412yescomplemented
12C29×#546—22no—
13C29×#546—22no—
14C29×#540—22no—
15C29×#535—21no—
16C29×#533C2211yescharacteristic
17C29×#532—21no—
18C29×#532—21no—
19C2×C29×#127C2211yescharacteristic
20C29×#518—21no—
21C4×#41×C29C2211yescharacteristic
22C29×#431C2211yescharacteristic
23C29×#423C2211yescharacteristic
24C2×C29×C4⋊C8C2211yescharacteristic
25C2×C29×#104—21no—
26C2×C29×#102—22no—
27C4×C4⋊C4×C29C2211yescharacteristic
28C29×#339—21no—
29C29×#333—21no—
30C29×#332—21no—
31C29×#331—22no—
32C29×#328—22no—
33C29×Q8⋊C8—21no—
34C29×D4⋊C8—21no—
35C2×#41×C29—22no—
36C2×#41×C29—22no—
37C2×#41×C29D411yescharacteristic
38C22×D4×C29—21no—
39C22×D4×C29—21no—
40C22×D4×C29D412yes—
41C2×M16×C29—21no—
42C22×C8×C29—21no—
43C29×C4⋊Q8D411yescharacteristic
44C29×C4⋊Q8D411yescharacteristic
45C29×#127—22no—
46C29×#127—21no—
47C29×#127—21no—
48C29×#127C2×C412yes—
49C29×#127D412yes—
50C29×#125—21no—
51C29×#124—22no—
52C29×#124—22no—
53C29×#124—22no—
54C29×#123—24no—
55C29×#123—24no—
56C29×C22⋊Q8—21no—
57C29×C22⋊Q8D412yes—
58C29×#121—22no—
59C29×#121—22no—
60C29×#121—22no—
61C29×#121—24no—
62C29×#121—24no—
63C29×#121—22no—
64C29×#120—24no—
65C4×Q8×C29—21no—
66C4×Q8×C29C2×C411yescharacteristic
67C4×Q8×C29C2×C412yes—
68C4×Q8×C29D411yescharacteristic
69C4×D4×C29—22no—
70C4×D4×C29—22no—
71C4×D4×C29—22no—
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C4×D4×C29—22no—
75C4×D4×C29—22no—
76C4×D4×C29—22no—
77C4×D4×C29C2×C411yescharacteristic
78C4×D4×C29D411yescharacteristic
79C29×#117—21no—
80C29×#117—21no—
81C29×#117D411yescharacteristic
82C2×C4⋊C4×C29—21no—
83C2×C22⋊C4×C29—24no—
84C2×C42×C29—21no—
85C2×C42×C29—21no—
86C2×C42×C29C2311yescharacteristic
87C29×C4⋊C8—21no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8—21no—
90C29×C4⋊C8—21no—
91C29×C4⋊C8—21no—
92C29×#104—42no—
93C29×#102—44no—
94C29×C22⋊C8—21no—
95C4×C8×C29—21no—
96C29×#95—21no—
97C24×C29—22no—
98#41×C29—21no—
99#41×C29—21no—
100#41×C29—21no—
101#41×C29—21no—
102#41×C29—84no—
103#41×C29—82no—
104#41×C29—82no—
105C2×Q8×C29—21no—
106C2×Q8×C29C22⋊C411yescharacteristic
107C2×Q8×C29C22⋊C412yes—
108C2×D4×C29—21no—
109C2×D4×C29—24no—
110C2×D4×C29—24no—
111C2×D4×C29—22no—
112C2×D4×C29—22no—
113C2×D4×C29—22no—
114C2×D4×C29—22no—
115C2×D4×C29—22no—
116C2×D4×C29—42no—
117C2×D4×C29—42no—
118C2×D4×C29—41no—
119C2×D4×C29—41no—
120C2×D4×C29—41no—
121C2×D4×C29—41no—
122C2×D4×C29—82no—
123C2×D4×C29C22⋊C411yescharacteristic
124C2×D4×C29C22⋊C414yes—
125C22×C4×C29—24no—
126C22×C4×C29—24no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—41no—
131C22×C4×C29C2×D411yescharacteristic
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29C2×D411yescharacteristic
134M16×C29—41no—
135M16×C29—41no—
136C2×C8×C29—42no—
137C2×C8×C29—41no—
138C2×C8×C29—41no—
139C2×C8×C29—41no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—22no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—22no—
147C4⋊C4×C29—22no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29C22⋊C411yescharacteristic
150C4⋊C4×C29C22⋊C411yescharacteristic
151C4⋊C4×C29C22⋊C412yes—
152C22⋊C4×C29—24no—
153C22⋊C4×C29—24no—
154C22⋊C4×C29—24no—
155C22⋊C4×C29—24no—
156C22⋊C4×C29—21no—
157C22⋊C4×C29—22no—
158C22⋊C4×C29—21no—
159C22⋊C4×C29—21no—
160C42×C29—21no—
161C42×C29—22no—
162C42×C29—21no—
163C42×C29—21no—
164C42×C29—41no—
165C42×C29—41no—
166C42×C29C22×C411yescharacteristic
167C42×C29C2×D411yescharacteristic
168C42×C29C2×D411yescharacteristic
169C42×C29C2×D411yescharacteristic
170#8426C2911yesmaximal, characteristic, direct product factor, Sylow
171C23×C29—24no—
172C23×C29—21no—
173C23×C29—42no—
174C23×C29—42no—
175C23×C29—82no—
176C23×C29—82no—
177C23×C29#12011yescharacteristic
178Q8×C29—21no—
179Q8×C29—21no—
180Q8×C29—42no—
181Q8×C29—41no—
182Q8×C29—41no—
183D4×C29—21no—
184D4×C29—21no—
185D4×C29—44no—
186D4×C29—44no—
187D4×C29—41no—
188D4×C29—41no—
189D4×C29—42no—
190D4×C29—42no—
191D4×C29—42no—
192D4×C29—42no—
193D4×C29—42no—
194D4×C29—42no—
195D4×C29—82no—
196D4×C29—84no—
197D4×C29—84no—
198C2×C4×C29—21no—
199C2×C4×C29—21no—
200C2×C4×C29—21no—
201C2×C4×C29—21no—
202C2×C4×C29—21no—
203C2×C4×C29—22no—
204C2×C4×C29—22no—
205C2×C4×C29—41no—
206C2×C4×C29—42no—
207C2×C4×C29—41no—
208C2×C4×C29—41no—
209C2×C4×C29—41no—
210C2×C4×C29—41no—
211C2×C4×C29—42no—
212C2×C4×C29—84no—
213C2×C4×C29—84no—
214C2×C4×C29—81no—
215C2×C4×C29—81no—
216C2×C4×C29C2×C22⋊C411yescharacteristic
217C2×C4×C29C2×C22⋊C411yescharacteristic
218C2×C4×C29C2×C22⋊C411yescharacteristic
219C2×C4×C29#12011yescharacteristic
220C2×C4×C29#12011yescharacteristic
221C2×C4×C29#12011yescharacteristic
222C2×C4×C29#13511yescharacteristic
223C2×C4×C29#13511yescharacteristic
224C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
225C2×C4×C29#13711yescharacteristic
226C8×C29—81no—
227C8×C29—81no—
228C8×C29—81no—
229#3508C2×C2911yescharacteristic
230#1982C2×C2911yescharacteristic, complemented
231#1806C2×C2911yescharacteristic, complemented
232#1550C2×C2911yescharacteristic, complemented
233#1545C2×C2911yescharacteristic, complemented
234#1503C2×C2911yescharacteristic, complemented
235#1477C2×C2911yescharacteristic, complemented
236C22×C29—21no—
237C22×C29—21no—
238C22×C29—41no—
239C22×C29—44no—
240C22×C29—41no—
241C22×C29—44no—
242C22×C29—41no—
243C22×C29—44no—
244C22×C29—162no—
245C22×C29—162no—
246C22×C29#37911yescharacteristic
247C22×C29#44911yescharacteristic
248C22×C29#45211yescharacteristic
249C4×C29—21no—
250C4×C29—21no—
251C4×C29—21no—
252C4×C29—41no—
253C4×C29—42no—
254C4×C29—41no—
255C4×C29—42no—
256C4×C29—41no—
257C4×C29—82no—
258C4×C29#41611yescharacteristic
259C4×C29#41711yescharacteristic
260C4×C29#44911yescharacteristic
261C4×C29#45211yescharacteristic
262C4×C29#45311yescharacteristic
263C4×C29#45511yescharacteristic
264#559—21no—
265#559C4×C2912yescomplemented
266#550—21no—
267#550C4×C2912yescomplemented
268#546—22no—
269#546—22no—
270#540—22no—
271#535—21no—
272#533C22×C2911yescharacteristic
273#532—21no—
274#532—21no—
275C2×#127C22×C2911yescharacteristic
276#518—21no—
277C4×#41C22×C2911yescharacteristic
278#431C22×C2911yescharacteristic
279#423C22×C2911yescharacteristic
280C2×C4⋊C8C22×C2911yescharacteristic
281C2×#104—21no—
282C2×#102—22no—
283C4×C4⋊C4C22×C2911yescharacteristic
284#339—21no—
285#333—21no—
286#332—21no—
287#331—22no—
288#328—22no—
289Q8⋊C8—21no—
290D4⋊C8—21no—
291C2×C29—21no—
292C2×C29—21no—
293C2×C29—81no—
294C2×C29—84no—
295C2×C29#178811yescharacteristic
296C2×C29#179211yescharacteristic
297C2×C29#179511yescharacteristic
298C2×#41—22no—
299C2×#41—22no—
300C2×#41D4×C2911yescharacteristic
301C22×D4—21no—
302C22×D4—21no—
303C22×D4D4×C2912yes—
304C2×M16—21no—
305C22×C8—21no—
306C4⋊Q8D4×C2911yescharacteristic
307C4⋊Q8D4×C2911yescharacteristic
308#127—22no—
309#127—21no—
310#127—21no—
311#127C2×C4×C2912yes—
312#127D4×C2912yes—
313#125—21no—
314#124—22no—
315#124—22no—
316#124—22no—
317#123—24no—
318#123—24no—
319C22⋊Q8—21no—
320C22⋊Q8D4×C2912yes—
321#121—22no—
322#121—22no—
323#121—22no—
324#121—24no—
325#121—24no—
326#121—22no—
327#120—24no—
328C4×Q8—21no—
329C4×Q8C2×C4×C2911yescharacteristic
330C4×Q8C2×C4×C2912yes—
331C4×Q8D4×C2911yescharacteristic
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4C2×C4×C2911yescharacteristic
341C4×D4D4×C2911yescharacteristic
342#117—21no—
343#117—21no—
344#117D4×C2911yescharacteristic
345C2×C4⋊C4—21no—
346C2×C22⋊C4—24no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42C23×C2911yescharacteristic
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355#104—42no—
356#102—44no—
357C22⋊C8—21no—
358C4×C8—21no—
359#95—21no—
360C29#842611yescharacteristic, direct product factor, Sylow
361C24—22no—
362#41—21no—
363#41—21no—
364#41—21no—
365#41—21no—
366#41—84no—
367#41—82no—
368#41—82no—
369C2×Q8—21no—
370C2×Q8C22⋊C4×C2911yescharacteristic
371C2×Q8C22⋊C4×C2912yes—
372C2×D4—21no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—82no—
387C2×D4C22⋊C4×C2911yescharacteristic
388C2×D4C22⋊C4×C2914yes—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—41no—
395C22×C4C2×D4×C2911yescharacteristic
396C22×C4C2×D4×C2911yescharacteristic
397C22×C4C2×D4×C2911yescharacteristic
398M16—41no—
399M16—41no—
400C2×C8—42no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4C22⋊C4×C2911yescharacteristic
414C4⋊C4C22⋊C4×C2911yescharacteristic
415C4⋊C4C22⋊C4×C2912yes—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—21no—
421C22⋊C4—22no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C42—21no—
425C42—22no—
426C42—21no—
427C42—21no—
428C42—41no—
429C42—41no—
430C42C22×C4×C2911yescharacteristic
431C42C2×D4×C2911yescharacteristic
432C42C2×D4×C2911yescharacteristic
433C42C2×D4×C2911yescharacteristic
434C23—24no—
435C23—21no—
436C23—42no—
437C23—42no—
438C23—82no—
439C23—82no—
440C23C29×#12011yescharacteristic
441Q8—21no—
442Q8—21no—
443Q8—42no—
444Q8—41no—
445Q8—41no—
446D4—21no—
447D4—21no—
448D4—44no—
449D4—44no—
450D4—41no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—84no—
460D4—84no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—84no—
476C2×C4—84no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4C2×C22⋊C4×C2911yescharacteristic
480C2×C4C2×C22⋊C4×C2911yescharacteristic
481C2×C4C2×C22⋊C4×C2911yescharacteristic
482C2×C4C29×#12011yescharacteristic
483C2×C4C29×#12011yescharacteristic
484C2×C4C29×#12011yescharacteristic
485C2×C4C29×#13511yescharacteristic
486C2×C4C29×#13511yescharacteristic
487C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
488C2×C4C29×#13711yescharacteristic
489C8—81no—
490C8—81no—
491C8—81no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—44no—
496C22—41no—
497C22—44no—
498C22—41no—
499C22—44no—
500C22—162no—
501C22—162no—
502C22C29×#37911yescharacteristic
503C22C29×#44911yescharacteristic
504C22C29×#45211yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—42no—
511C4—41no—
512C4—42no—
513C4—82no—
514C4C29×#41611yescharacteristic
515C4C29×#41711yescharacteristic
516C4C29×#44911yescharacteristic
517C4C29×#45211yescharacteristic
518C4C29×#45311yescharacteristic
519C4C29×#45511yescharacteristic
520C2—21no—
521C2—21no—
522C2—84no—
523C2—81no—
524C2C29×#178811yescharacteristic
525C2C29×#179211yescharacteristic
526C2C29×#179511yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3508C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C29×#1982C2semidirect
3. C29×#1806C2semidirect
4. C29×#1550C2semidirect
5. C29×#1545C2semidirect
6. C29×#1503C2semidirect
7. C29×#1477C2semidirect
9. C29×#559C4semidirect
11. C29×#550C4semidirect
170. #8426C29direct (N × H)
230. #1982C2×C29semidirect
231. #1806C2×C29semidirect
232. #1550C2×C29semidirect
233. #1545C2×C29semidirect
234. #1503C2×C29semidirect
235. #1477C2×C29semidirect
265. #559C4×C29semidirect
267. #550C4×C29semidirect
360. C29#8426direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C29×#35082
C29×#19822
C29×#18062
C29×#15502
C29×#15452
C29×#15032
C29×#14772
#842629